1. The Field of the Invention
The present invention relates to a method of making highly homogeneous low-stress single crystals with a predetermined orientation by immersing a single crystal in a melt and slowly drawing the single crystal out of the melt while crystallization is occurring, to an apparatus for performing the method of making the single crystals, and to the single crystals made by the method and their uses.
2. Related Art
The use of crystalline material for making lenses and optical elements is known. Particularly integrated circuits made by photolithography require large-volume calcium fluoride single crystals, which are permeable to short wavelength light up to a working wavelength of about 130 nm. Increasing requirements for increasingly higher integration density result in further miniaturization of structural elements and require forming increasingly smaller structures in the photolithograph processing. For these reasons immersion techniques used in microscopy have already been suggested for making computer chips. In these methods the optical element, through which the projected light from the objective passes, is dipped in an immersion liquid. In this way it is possible to increase the aperture angle and thus the resolution and the depth of focus. However the size of the actual objective aperture angle depends on the index of refraction of its terminal lens or front lens in the projection system. The index of refraction of CaF2 of 1.5 does not meet the requirements of the 32-nm technology points. Highly refractive crystals, especially oxides of rare earths, such as YAG, LuAG, and GGG (Gadolinium-Gallium-Garnet), which all have an index of refraction greater than 1.75, are generally used for those applications. These types of crystals are economical crystals used for making laser rods. When they are used for making laser rods, they are doped during the growing process. Laser rods with a maximum 10 mm diameter are drilled out from low-stress regions of the drawn crystals. Since these laser rods have the above-described reduced dimensions, crystal diameters of about 50 mm have already been obtained. These dimensions are essentially too small for making lens blanks for projection objectives of a stepper and their optical quality (index of refraction uniformity, stress birefringence, DUV transmission) is completely unsatisfactory.
The making of this sort of crystal generally occurs by drawing or by dipping a crystal seed in a melt of crystal raw material and by slowly drawing the crystal seed from the melt while crystallizing to form the solid crystal. The so-called Czochralski method, with which single crystals of high melting oxides, such as sapphire (Al2O3), garnet, YAG (Y3Al5O12), and spinel (MgAl2O4) are made, is usually used in industrial scale production. The crystals made in commercially available apparatus are drawn from iridium crucibles at melting temperatures up to 2000° C.
Up to now however this technology cannot produce crystals that meet the requirements for optical elements in lithography steppers. These optical elements must have diameters of at least 100 mm, especially 150 to 200 mm and, at the same time, the required optical uniformity parameters, such as a stress-induced birefringence of less than 1 nm/cm at 193 nm and an index of refraction uniformity of Δn less than 1 ppm.
If grown crystals are used for the above-described application in photolithography, they must have diameters of up to about 200 nm or larger and the required optical uniformity properties over at least 80% of the crystal diameter and at least 100 mm of the cylindrical product crystal. Only then may e.g. lens blanks with a diameter of about 150 mm and a thickness of about 40 mm be made from the grown crystals. Furthermore this sort of crystal must be economical and must have reproducible quality.
Usually a convex growth cone, which extends into the melt, arises in a growing crystal during growth of the crystal from an oxidic melt according to the Czochralski method or a method derived from it, such as the so-called “Top Speed Solution Growth Method” (TSSG). This cone is produced, above all, because the energies released during crystallization is conducted away by the crystal. The curvature of the growing face of the crystal depends on the thermal properties of the crystal and the melt and their interaction.
Now it is known that the convection flow in the melt present in the crucible is poor, so that heating by means of a heating element arranged on or in the crucible wall produces a free or basic convection. The melt heated at the crucible wall rises and the slightly cooler melt in the center of the crucible sinks downward. A circular, rotationally symmetric free convection from the outside to the inside is produced in this way. On the other hand, the upper part of the melt is rotated together with the rotating crystal extending into the melt, so that the denser melt cooled at the crystal is conducted by the centrifugal forces to the crucible wall and sinks there until captured by the free convection flow and again conducted to the center of the crucible. Thus the rotating crystal produces a forced convection, which behaves in an opposite manner to the above-described free convection, which is produced by heating. The forced and free convection are approximately mirror symmetric to each other in relation to the planar crucible cross-section.
However these opposing flow and convection processes are unstable and especially easily changed by changing the temperature profile in the crucible or the rotation speed. The resulting fluctuations and/or instabilities of the temperature act directly on the growth process at the phase boundaries between the crystal and melt and bring about fluctuations in the growth speed, which produce troublesome contrasting strips (growth strips or striations) in the finished crystal. Such contrast strips are produced by fluctuations of the lattice constants and thus the index of refraction. They impair the optical uniformity of the crystal. They are observable without more by known observation methods, such as examination between crossed polarizers or X-ray methods.
It has now been shown that the condensation heat released by condensation at the phase boundary surface produces temperature oscillations and thus the undesirable growth strips, which are still observable in the finished crystal. If a crystal of this sort is cut along its center axis, then a fishtail pattern produced by so-called striations produced by temperature fluctuations of any sort, is visible, especially in observation between crossed polarizers. If an optical element, such as a lens, is made from this sort of crystal, then it has a ring-like arrangement of differing refractive indexes similar to the growth rings of a tree. Thus a lens of this type is no longer useable for the above-described application. These types of structure defects characterized as growth strips arise themselves in unitary systems, in which distribution inhomogeneities do not occur. However it has been shown that this strip formation arises by changes and/or fluctuations in the growth conditions, especially the growing speed, which are ascribed to changes in the growing speed v and the hypothetical diffusion boundary layer thickness, δ, wherein the diffusion coefficient is a constant. These striations are formed by complex, currently not understood fluctuations in the growing speed and the transport processes at the growth front.
Currently it is not possible to keep the behavior of the convection reproducible over the entire growth period due to the competition between natural convention and forced convection. If natural convection dominates the convection processes, a convex phase boundary arises with the development of growth facets and a tendency to form growth strips. If forced convection dominates the convection processes, an especially undesirable concave phase boundary arises with all the negative effects of growth defects.
The current control methods for drawing speed, rotation speed, and optionally heating power depending on the crystal weight, which are practiced according to the state of the art, have not been sufficient for that purpose.
Many experiments for improving the uniformity of the crystals that have been grown have already been undertaken. Thus DD 290 921 described improvements in the uniformity of the garnet crystals made according to the Czocharalski method, when they are grown so that the phase boundary surface has an inclination angle, relative to the crystallographic (111) plane of 44±5° or 0±10° C. This phase boundary inclination angle is kept constant during the growing process by variation of the rotation speed.
DE 390 59 66 A1 describes growth of crystals for laser applications according to the Czochralski method, and of course especially of Nd:YAG crystals in the crystallographic (100)-direction or (111)-direction, in which the inclination angle of the phase boundary surface should be less than or equal to 35° for the (100)-direction and 44±5° for the (111)-direction. Here also the inclination angle should be maintained constant by variation of the rotation speed, once it is set. This procedure was selected, since all attempts to adjust a planar phase boundary were viewed as clever in the state of the art at that time, since the course of the phase boundary could not be reproducibly adjusted. Although this method already produces improvements in the uniformity properties of the crystals, the crystals still do not have the uniformity required for optical elements.